I've checked on multiple decks and two separate devices. Ante 1 skip tags are always handy tag and garbage tag on my iPhone 12 Pro Max (iOS 17). On my iPhone 14 (iOS 18), they do change when starting a new run. I can reset and they are different every time. Not sure if it is because of iOS 17 or if there is something else.
Edit: added videos from both devices.
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Edit 2: Tested on my iPad Air on iOS 18 beta and it has the same issue as my iPhone 12 Pro Max